Topic 73 Chord Theorems

Front

What is a chord in a circle?

Back

A chord is a line segment with both endpoints on the circle.

Front

What is the relationship between a diameter and a chord in a circle?

Back

A diameter is the longest chord in a circle and is perpendicular to any chord that it bisects.

Front

If a diameter is perpendicular to a chord, what can be said about the segments of the chord?

Back

The diameter bisects the chord into two equal segments.

Front

What is the formula to find the length of a chord given the radius and the distance from the center to the chord?

Back

Length of chord = 2 * √(r² - d²), where r is the radius and d is the distance from the center to the chord.

Front

What does it mean if a chord is bisected?

Back

It means that the chord is divided into two equal parts.

Front

If a chord is 8 units long, what is the length of each segment if it is bisected?

Back

Each segment is 4 units long.

Front

What is the definition of a tangent line in relation to a circle?

Back

A tangent line is a line that touches the circle at exactly one point.

Front

How can you determine if a line is a tangent to a circle?

Back

If the line is perpendicular to the radius at the point of contact, it is a tangent.

Front

What is the relationship between a chord and a tangent at the point of contact?

Back

A tangent is perpendicular to the radius drawn to the point of contact on the circle.

Front

What is the significance of the angle subtended by a chord at the center of the circle?

Back

The angle subtended by a chord at the center is twice the angle subtended at any point on the remaining part of the circle.